Section 8: Inflation and the Origin of Structure

On the largest cosmological scales, the universe appears to be approximately homogeneous and isotropic. That is, it looks approximately the same in all directions. On smaller scales, however, we see planets, stars, galaxies, clusters of galaxies, superclusters, and so forth. Where did all of this structure come from, if the universe was once a smooth distribution of hot gas with a fixed temperature?

The temperature of the fireball that emerged from the Big Bang must have fluctuated very slightly at different points in space (although far from enough to solve the horizon problem). These tiny fluctuations in the temperature and density of the hot gas from the Big Bang eventually turned into regions of a slight overdensity of mass and energy. Since gravity is attractive, the overdense regions collapsed after an unimaginably long time to form the galaxies, stars, and planets we know today. The dynamics of the baryons, dark matter, and photons all played important and distinct roles in this beautiful, involved process of forming structure. Yet, the important point is that, over eons, gravity amplified initially tiny density fluctuations to produce the clumpy astrophysics of the modern era. From where did these tiny density fluctuations originate? In inflationary theory, the hot gas of the Big Bang arises from the oscillations and decay of the inflaton field itself. Therefore, one must find a source of slight fluctuations or differences in the inflaton's trajectory to its minimum, at different points in space. In our analogy with the ball on the hill, remember that inflation works like a different ball rolling down an identically shaped hill at each point in space. Now, we are saying that the ball must have chosen very slightly different trajectories at different points in space—that is, rolled down the hill in very slightly different ways.

Figure 28: Small fluctuations in density in the far left box collapse into large structures on the right in this computer simulation of the universe.

One source of fluctuations is quantum mechanics itself. The roll of the inflaton down its potential hill cannot be the same at all points in space, because small quantum fluctuations will cause tiny differences in the inflaton trajectories at distinct points. But because the inflaton's potential energy dominates the energy density of the universe during inflation, these tiny differences in trajectory will translate to small differences in local energy densities. When the inflaton decays, the different regions will then reheat the Standard Model particles to slightly different temperatures.

Who caused the inflation?

This leaves our present-day understanding of inflation with the feel of a murder mystery. We've found the body—decisive evidence for what has happened through the nearly uniform CMB radiation and numerous other sources. We have an overall framework for what must have caused the events, but we don't know precisely which suspect is guilty; at our present level of knowledge, many candidates had opportunity and were equally well motivated.

Figure 29: Typical string theories or supersymmetric field theories have many candidate scalar field inflatons.

In inflationary theory, we try to develop a watertight case to convict the single inflaton that was relevant for our cosmological patch. However, the suspect list is a long one, and grows every day. Theories of inflation simply require a scalar field with a suitable potential and some good motivation for the existence of that scalar and some rigorous derivation of that potential. At a more refined level, perhaps they should also explain why the initial conditions for the field were just right to engender the explosive inflationary expansion. Modern supersymmetric theories of particle physics, and their more complete embeddings into unified frameworks like string theory, typically provide abundant scalar fields.

While inflationary expansion is simple to explain, it is not simple to derive the theories that produce it. In particular, inflation involves the interplay of a scalar field's energy density with the gravitational field. When one says one wishes for the potential to be flat, or for the region over which it is flat to be large, the mathematical version of those statements involves MPlanck in a crucial way: Both criteria depend on MPlanck2 multiplied by a function of the potential. Normally, we don't need to worry so much about terms in the potential divided by powers of MPlanck because the Planck mass is so large that these terms will be small enough to neglect. However, this is no longer true if we multiply by MPlanck2. Without going into mathematical details, one can see then that even terms in the potential energy suppressed by a few powers of MPlanck can qualitatively change inflation, or even destroy it. In the analogy with the rolling ball on the hill, it is as if we need to make sure that the hilltop is perfectly flat with well-mown grass, and with no gophers or field mice to perturb its flat perfection with minute tunnels or hills, if the ball is to follow the inflation-causing trajectory on the hill that we need it to follow.

Figure 30: The LHC creates the highest-energy collisions on Earth, but these are irrelevant to Planck-scale physics.

In particle physics we will probe the physics of the TeV scale at the LHC. There, we will be just barely sensitive to a few terms in the potential suppressed by a few TeV. Terms in the potential that are suppressed by MPlanck are, for the most part, completely irrelevant in particle physics at the TeV scale. If we use the cosmic accelerator provided by the Big Bang, in contrast, we get from inﬂation a predictive class of theories that are crucially sensitive to quantum gravity or string theory corrections to the dynamics. This is, of course, because cosmic inflation involves the delicate interplay of the inflaton with the gravitational field.